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# Distribution of IQ Scores

IQ scores have u = 100 and o = 15. The distribution is normal. A new drug is touted as having the effect of raising IQ by 10 points and we recruit a sample of n = 36 people to test it on. Using a=.05, how much power will we have? Please show work.

What is the probability of randomly selecting a red haired person from this distribution below?

Grey Brown Blonde Black Red
Eyes Blue 2 14 6 11 9
Green 4 17 8 9 8
Brown 6 19 9 28 9

Using the above chart what is the probability of selecting a blue eyed blond from this distribution?

Given that the probability that Nancy will wear blue to class is 20% and the probability that Tim will wear blue to class is 30%. What is the probability that they will both wear blue to class on same day?

What is probability that one of them will wear blue to class?

I am having difficulty with my formula's. I am taking an online class and cannot get it right. Just need some guidance.

#### Solution Preview

1.

Power is the probability of rejecting the null hypothesis given that the alternative hypothesis is true. Let's first set up our two hypotheses:

H_0: u = 100
H_1: u > 100

The first step is to find the rejection region. Given that a = 0.05, we want the probability of falling into the rejection region to be 0.05, assuming the null hypothesis is true. For a one-tailed normal distribution, a = 0.05 corresponds to a z value of 1.645. Thus, we want to solve for X ...

#### Solution Summary

The probability of randomly selecting a red haired person form this distribution is given. The probability that one of them will wear blue to class is given.

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